The families who feel 'priced out of London'

Sarah (right) lives with her mother, father and four siblings in emergency council accommodation

Britain's welfare system is undergoing a radical reform. Changes introduced this week include a benefits cap that limits the total amount any working-age household receives to £500 a week. How is this affecting families in London, which has some of the highest rents in the country?

Like many other girls of her age, 16-year-old Sarah Counihan Sanchez spent the summer term studying hard for her GCSEs. But there is more than exam stress on her mind - she and her family are facing the threat of eviction from their home in Ealing.

"Sometimes I have good days, when I feel I'm alright," explains Sarah as she gathers up her books for her next exam.

"But I am actually seeing a counsellor at the moment due to me feeling very low and feeling that no-one cares. When I heard about the notice to evict us, I started to get very panicky because I thought, 'What am I going to do? It's in the middle of my exams'."

Sarah, her mother, father and four siblings, aged four, seven, 12 and 14 are currently housed in temporary three-bedroom accommodation by the local council. Sarah doesn't have a bedroom, so she sleeps in the front room with her sister - and they aren't able to stay there long-term.

In the last four-bedroom home they lived in, the private landlord charged £690 a week - well over the new £500-a-week cap.

Isabel, Sarah's mother says: "We were paying £225 a week from our own pockets and housing benefit topped up the rest."

Sarah's father is a bus driver

Although Isabel is unable to work due to health problems - she is waiting for back and hip surgery - her husband has a full-time job.

But his wages did not cover his family's housing costs, and even though he was entitled to financial support from the government, an administrative error with their housing benefit claim meant they fell into arrears, and the landlord threw them out.

Research by the Building and Social Housing federation showed recently, that 93% of new claimants for housing benefit were in working households.

I point out to Isabel that the government implemented these reforms to scale down an annual £210bn welfare bill. This includes a housing benefit bill which has increased 62% over the last decade.

Work and Pensions Secretary Iain Duncan Smith said housing benefit completely exploded under the last government - it doubled in 10 years and was set to rise by another £5bn a year.

Isabel agrees that the bill for housing benefit is too high and that much of the money went straight to private landlords.

"The money spent on housing benefit is criminal, but the answer should be to build more public sector owned housing... rather than that money going to a landlord."

Isabel says the new benefits cap prices the family out of living in the capital, where private rents have increased by 65% since 2001, according to the National Housing Federation.

"We feel it's like an ethnic cleansing of London, moving the poorer people out," she says.

Overcrowded conditions

One of the most controversial reforms is the reduction in financial support for those living in public sector accommodation with spare rooms - dubbed the "bedroom tax" by the opposition.

The government wants to encourage movement within the social rented sector so that people in overcrowded conditions can move into currently under-occupied homes.

Emmanuel and Tya Richards hope to do just that. The couple have both always worked and paid their rent in full from their earnings.

They live with their three children - aged eight, 10 and 12 - and Tya's 34-year-old sister, on the top floor of a brown-brick tower block in Brixton.

It is a two-bedroom flat and, because space is so limited, their 12-year-old son sleeps on the floor.

They think it's fair that people who have spare bedrooms and who are dependent on state support to pay the rent should be made to downsize.

Tya says: "Since I was 19 I've never expected anyone to help me. There are times when you do need help and the government do help to get you back on your feet but then you go back straight into employment. If there are people sitting in four-bed homes paid for by the taxpayer - I don't think that's right," she says.

Spare bedrooms

In nearby Battersea, 60-year old Fred Steer has a different problem. He's lived in his four-bedroom housing association house since 1998, but has been out of work for 12 years because of back problems.

Mr Steer paints models - a skill he learnt when he was in work

The government has been paying his rent in full for most of this time but under the new rules he has been told to start paying a contribution of £34 a week towards his housing costs as, with only one daughter living with him permanently, he is officially designated as having two spare bedrooms.

I ask Mr Steer if he has sympathy for families who need extra space.

"I do have sympathy because I myself used to live in a two-bedroom flat with my ex-wife and five children for 11 years, so yes I do have sympathy."

But Mr Steer says the problem is a shortage in the supply of social housing stock.

"Margaret Thatcher gave councils the right to sell off their properties to tenants. Not building new housing has basically created this situation," he says.

Five million council houses were built between 1946 and 1981, but only 250,000 have been built since.

Mr Steer is attempting to claim disability living allowance - so far unsuccessfully - but in the meantime is accumulating rent arrears which could ultimately lead to his eviction.

"I haven't been able to pay. I'm not able to resolve my financial difficulties because I can't work. The government are forcing us out of our own homes," he says.

Since the welfare reforms were brought in, in April 2013, rent arrears are up in different areas of the UK. One London borough - Southwark - has reported an increase of 25% and the city of Leeds has reported an increase of 50%.

Nina Robinson's documentary Welfare Britain - the New Reality will be broadcast on Assignment on the BBC World Service on 18 July at 11:06 GMT. Listen via BBC iPlayer radio or download a podcast.